Appraise the effectiveness of graphic models in management decision making.
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Discuss why modeling is an effective method
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, please complete Problems 14-15, 14-23, 14-27, and 14-29 14-15 Andy Lange, president of the University of South Wisconsin, is concerned with the declining business at the University Book Store. (See Problem 14-14 BELOW for details.) The students tell him that the prices are simply too high. Andy, however, has decided not to lower the prices. If the same conditions exist, what long-run market shares can Andy expect for the four bookstores? 14-14 The University of South Wisconsin has had steady enrollments over the past five years. The school has its own bookstore, called University Book Store, but there are also three private bookstores in town: Bill’s Book Store, College Book Store, and Battle’s Book Store. The university is concerned about the large number of students who are switching to one of the private stores. As a result, South Wisconsin’s president, Andy Lange, has decided to give a student three hours of university credit to look into the problem. The following matrix of transition probabilities was obtained At the present time, each of the four bookstores has an equal share of the market. What will the market shares be for the next period? University Bill’s College Battle’s UNIVERSITY 0.6 0.2 0.1 0.1 BILL’S 0 0.7 0.2 0.1 COLLEGE0.1 0.1 0.8 0 BATTLE ’S 0.05 0.050.1 0.8 14-23 John Jones of Bayside Laundry has been providing cleaning and linen service for rental condominiums on the Gulf coast for over 10 years. Currently, John is servicing 26 condominium developments. John’s two major competitors are Cleanco, which currently services 15 condominium developments, and Beach Services, which performs laundry and cleaning services for 11 condominium developments. Recently, John contacted Bay Bank about a loan to expand his business operations. To justify the loan, John has kept detailed records of his customers and the customers that he received from his two major competitors. During the past year, he was able to keep 18 of his original 26 customers. During the same period, he was able to get 1 new customer from Cleanco and 2 new customers from Beach Services. Unfortunately, John lost 6 of his original customers to Cleanco and 2 of his original customers to Beach Services during the same year. John has also learned that Cleanco has kept 80% of its current customers. He also knows that Beach Services will keep at least 50% of its customers. For John to get the loan from Bay Bank, he needs to show the loan officer that he will maintain an adequate share of the market. The officers of Bay Bank are concerned about the recent trends for market share, and they have decided not to give John a loan unless he will keep at least 35% of the market share in the long run. What types of equilibrium market shares can John expect? If you were an officer of Bay Bank, would you give John a loan? 14-27 As a result of a recent survey of students at the University of South Wisconsin, it was determined that the university owned bookstore currently has 40% of the market. (See Problem 14-14.) The other three bookstores, Bill’s, College, and Battle’s, each split the remaining initial market share. Given that the state probabilities are the same, what is the market share for the next period given the initial market shares? What impact do the initial market shares have on each store next period? What is the impact on the steady state market shares? 14-29 During a recent trip to her favorite restaurant, Sandy (owner of shop 1) met Chris Talley (owner of shop 7) (see Problem 14-28 BELOW). After an enjoyable lunch, Sandy and Chris had a heated discussion about market share for the quick-oil-change operations in their city. Here is their conversation Sandy: My operation is so superior that after someone changes oil at one of my shops, they will never do business with anyone else. On second thought, maybe 1 person out of 100 will try your shop after visiting one of my shops. In a month, I will have 99% of the market, and you will have 1% of the market. Chris: You have it completely reversed. In a month, I will have 99% of the market, and you will only have 1% of the market. In fact, I will treat you to a meal at a restaurant of your choice if you are right. If I am right, you will treat me to one of those big steaks at David’s Steak House. Do we have a deal? Sandy: Yes! Get your checkbook or your credit card. You will have the privilege of paying for two very expensive meals at Anthony’s Seafood Restaurant. (a) Assume that Sandy is correct about customers visiting one of her quick-oil-change shops. Will she win the bet with Chris? (b) Assume that Chris is correct about customers visiting one of his quick-oil-change shops. Will he win the bet? (c) Describe what would happen if both Sandy and Chris are correct about customers visiting their quick-oil-change operations. 14-28 Sandy Sprunger is part owner in one of the largest quick-oil-change operations for a medium-sized city in the Midwest. Currently, the firm has 60% of the market. There are a total of 10 quick lubrication shops in the area. After performing some basic marketing research, Sandy has been able to capture the initial probabilities, or market shares, along with the matrix of transition, which represents probabilities that customers will switch from one quick lubrication shop to another. These values are shown in the table on the next page: Initial probabilities, or market share, for shops 1 through 10 are 0.6, 0.1, 0.1, 0.1, 0.05, 0.01, 0.01, 0.01, 0.01, and 0.01. (a) Given these data, determine market shares for the next period for each of the 10 shops. (b) What are the equilibrium market shares? (c) Sandy believes that the original estimates for market shares were wrong. She believes that shop 1 has 40% of the market, and shop 2 has 30%. All other values are the same. If this is the case, what is the impact on market shares for next-period and equilibrium shares? (d) A marketing consultant believes that shop 1 has tremendous appeal. She believes that this shop will retain 99% of its current market share; 1% may switch to shop 2. If the consultant is correct, will shop 1 have 90% of the market in the long run? Data for Problem 14-28 To From 1 2 3 4 5 6 7 8 9 10 1 0.60 0.10 0.10 0.10 0.05 0.01 0.01 0.01 0.01 0.01 2 0.01 0.80 0.01 0.01 0.010.10 0.01 0.01 0.0 10.03 3 0.01 0.01 0.70 0.01 0.01 0.10 0.01 0.05 0.050.05 4 0.01 0.01 0.01 0.90 0.01 0.01 0.01 0.01 0.01 0.02 5 0.01 0.01 0.01 0.10 0.80 0.01 0.03 0.01 0.01 0.01 6 0.01 0.01 0.01 0.01 0.01 0.91 0.01 0.01 0.01 0.01 7 0.01 0.01 0.01 0.01 0.01 0.10 0.70 0.01 0.10 0.04 8 0.01 0.01 0.01 0.01 0.01 0.100.03 0.80 0.01 0.01 9 0.01 0.01 0.01 0.01 0.01 0.10 0.01 0.10 0.70 0.04 10 0.010.01 0.01 0.01 0.01 0.10 0.10 0.05 0.00 0.70